LED system and method

ABSTRACT

Embodiments provide an LED comprising a quantum well region operable to generate light and a substrate having an interface with the quantum well region, wherein light generated by the quantum well region traverses the interface to enter the substrate and exit the LED through an exit face of the substrate. The exit face may be opposite from and a distance from the interface, with some portion or all of this LED being shaped to optimize the light extraction efficiency of the device. The exit face can have at least 70% of a minimum area necessary to conserve brightness for a desired half-angle of light. Sidewalls of the LED may be positioned and shaped so that rays incident on a sidewall reflect to the exit face with an angle of incidence at the exit face at less than or equal to a critical angle at the exit face.

RELATED APPLICATIONS

This application claims the benefit of priority under 35 U.S.C. 119(e)to U.S. Provisional Patent Application No. 60/827,818, entitled “SHAPEDLIGHT EMITTING DIODES”, to Dung T. Duong et al., filed Oct. 2, 2006, andto U.S. Provisional Patent Application No. 60/881,785, entitled “SYSTEMAND METHOD FOR A SHAPED SUBSTRATE LED”, to Dung T. Duong et al., filedJan. 22, 2007, both of which are hereby fully incorporated by referenceherein.

TECHNICAL FIELD OF THE INVENTION

This disclosure regards light emitting diodes (“LEDs”). Moreparticularly, embodiments of systems and methods described herein relateto increasing or controlling light output of an LED. Even moreparticularly, embodiments relate to increasing or controlling lightoutput of an LED by shaping portions of the LED substrate.

BACKGROUND

Light emitting diodes (“LEDs”) are ubiquitous in electronics. They areused in digital displays, lighting systems, computers and televisions,cellular telephones and a variety of other devices. Developments in LEDtechnology have led to methods and systems for the generation of whitelight using one or more LEDs. Developments in LED technology have led toLEDs that generate more photons and thus more light than previously. Theculmination of these two technological developments is that LEDs arebeing used to supplement or replace many conventional lighting sources,e.g. incandescent, fluorescent or halogen bulbs, much as the transistorreplaced the vacuum tube in computers.

LEDs are produced in a number of colors including red, green and blue.One method of generating white light involves the use of red, green andblue LEDs in combination with one another. A lighting source that ismade of combinations of red, green and blue (RGB) LEDs will produce whatis perceived as white light by the human eye. This occurs because thehuman eye has three types of color receptors, with each type sensitiveto either blue, green or red colors.

A second method of producing white light from LED sources is to createlight from a single-color (e.g. blue), short wavelength LED, and impingea portion of that light onto phosphor or similar photon conversionmaterial. The phosphor absorbs the higher energy, short wavelength lightwaves, and re-emits lower energy, longer wavelength light. If a phosphoris chosen that emits light in the yellow region (between green and red),for example, the human eye perceives such light as white light. Thisoccurs because the yellow light stimulates both the red and greenreceptors in the eye. Other materials, such as nano-particles or othersimilar photo-luminescent materials, may be used to generate white lightin much the same way.

White light may also be generated utilizing an ultraviolet (UV) LED andthree separate RGB phosphors. White light may also be generated from ablue LED and a yellow LED and may also be generated utilizing blue,green, yellow and red LEDs in combination.

Current industry practice for construction of LEDs is to use a substrate(typically either single-crystal Sapphire or Silicon Carbide), ontowhich is deposited layers of materials such as GaN or InGaN. One or morelayers (e.g. GaN or InGaN) may allow photon generation and currentconduction. Typically, a first layer of Gallium Nitride (GaN) is appliedto the surface of the substrate to form a transition region from thecrystal structure of the substrate to the crystal structure of dopedlayers allowing for photon generation or current conduction. This istypically followed by an N-doped layer of GaN. The next layer can be anInGaN, AlGaN, AlInGaN or other compound semiconductor material layerthat generates photons and that is doped with the needed materials toproduce the desired wavelength of light. The next layer is typically a Pdoped layer of GaN. This structure is further modified by etching anddeposition to create metallic sites for electrical connections to thedevice.

During the operation of an LED, as in a traditional diode, extraelectrons move from an N-type semiconductor to electron holes in aP-type semiconductor. In an LED, photons are released in the compoundsemiconductor layer to produce light during this process.

In a typical manufacturing process, the substrate is fabricated in waferform and the layers are applied to a surface of the wafer. Once thelayers are doped or etched and all the features have been defined usingthe various processes mentioned, the individual LEDs are separated fromthe wafer. The LEDs are typically square or rectangular with straightsides. This can cause significant efficiency losses and can cause theemitted light to have a poor emission pattern. A separate opticaldevice, such as a plastic dome, is often placed over the LED to achievea more desirable output.

In nearly all LED applications, it is desirable to maximize light outputfor a given power input, a quantity often expressed in lumens per watt(lm/W) for white light and longer wavelength light, or milliwatts perwatt (mW/W) for shorter wavelength light such as blue. Existing LEDtechnologies may attempt to increase this ratio, typically referred toas “overall efficiency” or “wall-plug efficiency.” However, existing LEDtechnologies still suffer poor overall efficiency and low extractionefficiency.

SUMMARY

This disclosure regards an LED having a substrate shaped to achievegreater efficiency than previous LEDs. The sidewalls of embodiments ofthe LED may be shaped so as to maximize the light output of the LEDusing total internal reflection and can be shaped to achieve a desiredintensity distribution. Additionally, the exit face of the LED may beselected to conserve radiance.

One embodiment includes a method of manufacturing an LED comprisingdetermining a size of an exit face of a shaped substrate portion of theLED that has at least 70% of a minimum area necessary to conserveradiance for a desired half-angle of light projected from the LED;determining a distance between the exit face and an interface betweenthe shaped substrate portion and a quantum well region of the LED;determining shapes and positions of a set of sidewalls of the shapedsubstrate portion of the LED so that each sidewall is positioned andshaped to cause at least a majority of rays having a straighttransmission path from the interface to that sidewall to reflect to theexit face with an angle of incidence at the exit face at less than orequal to a critical angle at the exit face; and forming the substrateportion of the LED in accordance with the determined size of the exitface, shapes and positions of the set of sidewalls and distance betweenthe exit face and the interface.

Another embodiment comprises a method of shaping an LED comprisingproviding a wafer comprising a substrate and one or more layers for aquantum well region of the LED and grinding the substrate to form ashaped substrate portion of the LED. The shaped substrate portion cancomprise an exit face opposite from and a distance from an interfacewith the quantum well region of the LED, the exit face having at least70% of a minimum area necessary to conserve radiance for a desiredhalf-angle of light projected from the shaped substrate; and a set ofsidewalls, wherein each sidewall is positioned and shaped so that atleast a majority of rays having a straight transmission path from theinterface to that sidewall reflect to the exit face with an angle ofincidence at the exit face of less than or equal to a critical angle atthe exit face.

Yet another embodiment of shaping an LED can comprise providing a wafercomprising a substrate and one or more layers for a quantum well regionof the LED and etching the substrate to form a shaped substrate portionof the LED. The shaped substrate portion can comprise an exit faceopposite from and a distance from and interface with the quantum wellregion of the LED, the exit face having at least 70% of a minimum areanecessary to conserve radiance for a desired half-angle of lightprojected from the shaped substrate and a set of sidewalls, wherein eachsidewall is positioned and shaped so that at least a majority of rayshaving a straight transmission path from the interface to that sidewallreflect to the exit face with an angle of incidence at the exit face ofless than or equal to a critical angle at the exit face.

Yet another embodiment can comprise a method of manufacturing an LEDcomprising providing a substrate and one or more layers for a quantumwell region of the LED and removing material from the substrate to forma shaped substrate portion of the LED. The shaped substrate portion cancomprise two or more exit faces having a combined area that is at least70% of a minimum area necessary to conserve radiance for a desiredhalf-angle of light projected from the LED and a set of sidewalls,wherein each sidewall is positioned and shaped so that at least amajority of rays having a straight transmission path from the interfaceto that sidewall reflect to an exit face of the two or more exit faceswith an angle of incidence at that exit face of less than or equal to acritical angle at that exit face.

Embodiments of systems and methods provide an LED that providestechnical advantages over the prior art by projecting light with adesired half-angle and light output profile, while conservingbrightness. Embodiments can provide, for example, light in 10 to 60degrees half angle (or other half angles) with high efficiency.

Embodiments provide yet another advantage by providing for light outputwith uniform or near uniform intensity distributions.

Yet another advantage provided by embodiments is that light can beprojected with a desired shape and light output profile.

BRIEF DESCRIPTION OF THE FIGURES

A more complete understanding of the embodiments and the advantagesthereof may be acquired by referring to the following description, takenin conjunction with the accompanying drawings in which like referencenumbers indicate like features and wherein:

FIGS. 1A-1B are diagrammatic representations of embodiments of LEDs;

FIG. 2 is a diagrammatic representation of a set of rays traveling froma point to surfaces at different distances from the point;

FIG. 3 provides a diagrammatic representation of a top view of anembodiment of an LED;

FIG. 4A is a diagrammatic representation of a cross-section of a modelof an LED for determining sidewall shapes;

FIG. 4B is a diagrammatic representation of an embodiment of a portionof a sidewall of an LED;

FIG. 4C is a diagrammatic representation illustrating that the facetsfor a sidewall can be defined using a computer program;

FIG. 4D is a diagrammatic representation of one embodiment of an LEDwith sidewalls shaped to cause TIR so that rays are reflected from thesidewalls to the exit surface;

FIG. 5 is a diagrammatic representation of one embodiment for estimatingeffective solid angle;

FIGS. 6A-6E are diagrammatic representations describing anotherembodiment for estimating effective solid angle;

FIG. 7 is a diagrammatic representation of one embodiment of a LED;

FIG. 8A-8B are diagrammatic representations of embodiments of an arrayof LEDs;

FIGS. 9A-9C are diagrammatic representations of embodiments of retainingdevices;

FIG. 10 is a functional representation of an embodiment of etching;

FIG. 11 is a functional representation of an embodiment of laserablation;

FIGS. 12A-12B are functional representation of an embodiment of sawing;

FIGS. 13A-13B are diagrammatic representations of an embodiment of awafer having had substrates shaped through sawing;

FIG. 14 is a diagrammatic representation of one embodiment of a LED; and

FIGS. 15A and 15B are diagrammatic representations of another embodimentof a wafer.

DETAILED DESCRIPTION

Embodiments are illustrated in the FIGURES, like numerals being used torefer to like and corresponding parts of the various drawings.

Embodiments of shaped substrate LEDs may be shaped so as to increase orshape the light emission from the LED. According to one embodiment, thesubstrate is shaped so that all or a supermajority of the lightgenerated by the quantum well region of the LED is transmitted out theexit face of the substrate of the LED. To this end, the exit face can besized to take into account principles of conservation of radiance. Inone embodiment, the exit face may be the minimum size that allows all ora supermajority of the light entering the substrate through theinterface between the quantum well region and the substrate to exit theexit face, thereby combining the desire to conserve radiance with thedesire to reduce size, particularly the size of the exit face.Additionally, the sidewalls of the substrate may be shaped so thatreflection or total internal reflection (“TIR”) causes light beamsincident on substrate sidewalls to reflect towards the exit face and beincident on the exit face with an angle less than or equal to thecritical angle. Consequently, light loss due to TIR at the exit face isreduced or eliminated. In a further embodiment, to insure that lightstriking a sidewall is reflected within the substrate and does not passthrough the sidewall, a sidewall or sidewalls of a substrate may also becoated with a reflective material that reflects light to prevent theexitance of light through the sidewall.

While theoretically 100% of the light generated by the quantum wells ofthe LED exits the exit face, various embodiments may cause lesseramounts of light to exit the exit face while still providing significantimprovements over prior LED light emissions. For example, light emittedfrom the exit surface of the LED may be emitted from the exit surfacewith a cone half angle of 10-60 degrees with approximately 79%efficiency (there is approximately a 21% efficiency loss due to fresnellosses for a silicon carbide substrate material of 2.73 index ofrefraction) with a desired intensity profile, exitance profile or otherlight output profile.

Fresnel losses (e.g. losses at the interface between two mediums such asat the exit face of an LED and air or other medium) occurs when lighttraverses from a medium of higher index to a medium of lower index.Normal incident fresnel losses are described by the equation:(N₁−N₂)²)/((N₁+N₂)²),

wherein N₁ and N₂ are the indices of refraction of the two mediums. Asan example, for an LED having a silicon carbide substrate, N₁=2.73(approximate IOR of silicon carbide), N₂=1 (approximate IOR of air),yielding Fresnel losses of approximately 21.5%. If the LED utilizes GaNin the quantum well region, Fresnel losses at the interface between thequantum well region (N₁=2.49) and the silicon carbide substrate(N₂=2.73) will be 0%. Fresnel losses at the exit face to air interfacemay be reduced or overcome with anti-reflective coatings.

As described above, the exit face of an LED substrate can be shaped toconserve radiance. The passage of light along an optic path, eitherwithin a single medium or from one medium to another, is governed by thelaw of Conservation of Radiance, also referred to as the BrightnessTheorem, which is expressed by the Etendue equation:

$\begin{matrix}{{{Entendue}\mspace{14mu}{Equation}\text{:}\mspace{11mu}\frac{\Phi_{1}}{N_{1}^{2}A_{1}\Omega_{1}}} = \frac{\Phi_{2}}{N_{2}^{2}A_{2}\Omega_{2}}} & \lbrack {{EQN}.\mspace{14mu} 1} \rbrack\end{matrix}$

-   Φ₁=light flux (lumens) of region 1-   N₁=IOR of medium of region 1-   A₁=area of entrance to region 1-   Ω₁=solid angle (steradians) that fully contains the light of region    1-   Φ₂=light flux (lumens) of region 2-   N₂=IOR of medium of region 2-   A₂=area of entrance to region 2-   Ω₂=solid angle (steradians) that fully contains the light of region    2

The area of the exit face of a shaped substrate can be selected toconserve radiance of light entering the substrate from the quantum wellsfor a desired half angle. Consequently, light can be emitted in adesired half angle with high efficiency. This is unlike traditional LEDsthat both emit light with a half angle that is undesirable for manyapplications, therefore requiring additional optical devices to shapethe light; and, emit a significant percentage of light through thesidewalls because the exit face is not large enough to conserveradiance; while also suffering absorption losses due to the light neverescaping the substrate.

Furthermore, the passage of light from a medium of one index ofrefraction to a medium of a different IOR is governed by Snell's Law.Snell's law defines the relationship between the angle of approach of alight ray as measured from the normal to the interface surface, and theangle of departure of that ray from the interface, as a function of theindices of refraction of both media.Snell's Law: N ₁ sin(Θ₁)=N ₂ sin(Θ₂)  [EQN. 2]

-   Θ₁=angle of incidence of ray approaching interface surface-   N₁=IOR of medium 1-   Θ₂=angle of refraction of ray departing interface surface-   N₂=IOR of medium 2

In the case of the passage of light from a medium of higher IOR to amedium of lower IOR, the maximum angle at which a light ray may strikethe interface surface between the media and still pass through theinterface is called the critical angle. Fundamentally, light originatingfrom the medium of higher IOR must approach the media interface atangles not exceeding the critical angle if the light is to pass throughthe interface and into the medium of lower IOR. For example, in an LEDcomprised of a substrate and a quantum well region, the substrate mediumand the quantum well medium may form an interface that light generatedby the quantum well regions traverses. Rays that approach at anglesgreater than the critical angle will be reflected back within the mediumof higher IOR at the interface between the media and will not pass intothe medium of lower IOR. This is referred to as total internalreflection (“TIR”).

In a typical LED, the quantum well region has an IOR of approximately2.49. When these layers are constructed on a sapphire substrate with anIOR of 1.77, the light that can be transmitted into the sapphire isinherently limited by the application of Snell's law and the BrightnessTheorem. For LEDs with a substrate of silicon carbide, which may have anIOR of approximately 2.73, the quantum well region has a lower IOR (e.g.approximately 2.49) than the silicon carbide, and therefore Snell's lawdoes not prohibit any of the generated light from passing into thesilicon carbide.

In traditional LEDs, a significant portion of light encountering asubstrate to air interface will be trapped in the substrate due to TIR.In some cases, a separate optical device (e.g. a solid plastic dome orlens) is used to increase the IOR of the medium into which light passesfrom the substrate, reducing TIR in the substrate. These separateoptical devices may still suffer from losses due to TIR, and theextraction efficiency of domes remains relatively low. Moreover, the useof a dome requires additional steps in manufacturing after the LED isformed. Embodiments of shaped substrate LEDs, on the other hand, can beshaped to minimize or eliminate light loss due to TIR at the exit faceof the substrate. According to one embodiment, the exit face of thesubstrate can be spaced from the interface with the quantum well regionby a distance so that none of the rays with a direct transmission pathto the exit face experience TIR at the exit face. Additionally, thesidewalls can be shaped to reflect rays encountering the sidewalls tothe exit face with an angle of incidence at the exit face that is lessthan the critical angle, thus allowing all internally reflected rays toexit the exit face of the LED substrate as well.

FIG. 1A is a diagrammatic representation of one embodiment of a LED 20including a substrate 10 and quantum well region 15 (that may compriseone or more layers or regions of doping). Quantum well region 15includes a light emitting region 25, typically a compound semiconductorsuch as InGaN or AlInGaP or AlGaN. Photons from quantum well region 15may enter substrate 10 through interface 50. LED 20 can be a wire bond,flip chip or other LED known or developed in the art. Both substrate 10and quantum well region 15 form sidewall 60, sidewall 65 or othersidewalls. In other words, quantum well region 15 is shaped inconformance with substrate 10. LED 20 further includes exit face 55 thatmay be substantially the same shape as, substantially parallel to andsubstantially rotationally aligned with interface 50 within thetolerance of the manufacturing process. The area of exit face 55 can bechosen to conserve brightness for a desired half angle according to theconservation of radiance (sometimes called the conservation ofbrightness) equation:

$\begin{matrix}{\frac{\Phi_{2}n_{1}^{2}A_{1}\Omega_{1}}{\Phi_{1}n_{2}^{2}\Omega_{2}} = A_{2}} & \lbrack {{EQN}.\mspace{14mu} 1} \rbrack\end{matrix}$

Φ₁=light flux traversing interface 50;

Φ₂=light flux exiting exit face 55, Φ₁=Φ₂ for conservation ofbrightness;

Ω₁=effective solid angle whereby light traverses interface 50;

Ω₂=effective solid angle whereby light leaves exit face 55;

A₁=area of interface 50;

A₂=area of exit face 55;

n₁=refractive index of material of substrate 10;

n₂=refractive index of substance external to substrate 10 (e.g. air orother medium).

A₂ represents the minimum surface area of exit face 55 such that lightis conserved per the above equation. Assume, for example: quantum wellregion 15 forms a 1 mm square so that interface 50 has an areaapproximately 1 mm square, n₁=1.77, n₂=1, Ω₁=3, Ω₂=1, then A₂ must be atleast 9.3987 mm² to conserve radiance (i.e. the minimum size of exitface 55 so that all of the light traversing interface 50 can be emittedfrom exit face 55 for a desired half angle). While in this example theeffective solid angles are given, methods for determining Ω₁ and Ω₂ fora desired half angle are discussed below in conjunction with FIGS.6A-6E. It should be noted that the square profile is a rectangularprofile with sides of equal length.

A₂ according to EQN. 1 is the minimum possible size for a given outputcone angle or Emission Half Angle to conserve radiance. Consequently, toconserve radiance, A₂ should be at least the size determined from EQN.1, but may be larger. For example, A₂ may be made slightly larger tocompensate for tolerances in the manufacturing process, errors in thesize or shape of quantum well region 15 or other factors.

In the case where A₂ is made larger than the value determined byequation 1, flux will be conserved, but exitance (defined as flux perunit area) may be reduced from the maximum attainable value.

To reduce the area of the exit face, however, it may be preferable thatA₂ be as small as possible. For example, A₂ may be within 5% of theminimum area needed to conserve radiance. If some light power (luminousflux) may be sacrificed, A₂ can be smaller than the size dictated by theconservation of radiance. As one example, for one embodiment having a 1mm by 1 mm square interface 50, exit face 55 can be 2.5 mm² to 5 mm²(e.g., 4.62 mm²). As another example, for an embodiment having 0.3mm×0.3 mm interface 50, exit face 55 can be 0.2 mm² to 0.5 mm² (e.g.,0.42 mm²). It should be noted, however, the size ranges provided in theprevious examples are provided by way of example only, and variousembodiments can have a variety of sizes smaller than or greater than theexample ranges. Preferably, however, A₂ is at least 70% of the value asdetermined by EQN. 1. Furthermore, the shape of exit face 55 may bedifferent than that of interface 50.

The distance between interface 50 and exit face 55 of substrate10—referred to as the “height” herein, though the distance may extend inother directions than the vertical—may be selected to reduce or minimizeTIR of light rays traveling directly from interface 50 to exit surface55. TIR occurs when light is incident on the surface with an angle ofincidence greater that critical angle, which is defined by:n ₁ sin(θ_(c))=n ₂ sin(90)  [EQN. 2]

where n₁=IOR of substrate 10;

n₂=IOR of the medium external to the exit face of substrate 10 (e.g.,air or other substance); and

θ_(c)=the critical angle.

For example, if n₁=1.77 and n₂=1, then θ_(c)=34.4 degrees. Accordingly,the height of substrate 10 can be selected to limit the critical angleof rays incident on exit surface 55 to a range between normal to exitsurface 55 and less than or equal to the critical angle.

Referring to FIGS. 2 and 3, FIG. 2 is a diagrammatic representation of aset of rays traveling from point 57 incident on a surface 55(represented as surfaces 55 a, 55 b and 55 c at different distances frompoint 57). In the example of surface 55 a, some rays (e.g., ray 56) areincident on surface 55 a at greater than the critical angle, causingloss of light due to TIR. In the example of surface 55 b, conversely,some rays that would be incident on surface 55 b at the critical angleor somewhat less than the critical angle (e.g., ray 57) will instead beincident on the sidewalls. Preventing loss of these rays, if desired,can cause the complexity of the sidewall design to increase. Moreover,the additional height requires more room to accommodate the LED (i.e.,because the LED is taller). Finally, in the case of surface 55 c, raysat or less than the critical angle are incident on surface 55 c whilerays that would be greater than the critical angle on exit surface 55 cinstead are incident on the sidewalls. TIR or reflection can be used todirect the rays incident on the sidewalls to exit surface 55 c asdiscussed below.

The limiting ray for selecting height, according to one embodiment, isthe ray that travels the longest straight line distance from interface50 to exit face 55 and is incident on exit face 55 at the criticalangle. There may be more than one ray that can be selected as thelimiting ray. In a square or rectangular configuration this is the raythat enters substrate 10 at a corner of interface 50 and travels in astraight line to the diagonally opposite corner of exit face 55 suchthat the ray would be incident on exit face 55 at the critical angle.

FIG. 3 provides a diagrammatic representation of a top view of substrate10 and of limiting ray 59 for a square configuration. While in thepreferred embodiment the height of substrate 10 is selected to limit thecritical angle of rays incident on exit face 55 to a range of betweennormal to exit face 55 and to less than or equal to the critical angle,other heights can be selected, though the use of other heights maydecrease the efficiency of LED 20. In one embodiment, the distancebetween the interface between the quantum well region and the substrateand the exit face of the substrate may be within 5% of the minimumheight that causes all rays with a straight transmission path from theinterface to the exit face to have an angle of incidence on the exitface at less than or equal to the critical angle.

Returning to FIG. 1A, with selected boundary conditions of the size andshape of interface 50, size and shape of exit face 55, distance betweeninterface 50 and exit face 55, the sidewalls (e.g., sidewall 60,sidewall 65 and other sidewalls) of substrate 10 can be shaped to directlight incident on the inner side of the sidewalls to exit face 55 toproduce a desired light output profile (e.g., an intensity profile,exitance profile or other light output profile). While for mostapplications the desired intensity profile is uniform or close touniform, other distribution profiles can be achieved by varying theheight and shapes of the sidewalls.

Broadly speaking, the sidewall shapes are determined so that any rayincident on a sidewall is reflected to exit face 55 and is incident onexit face 55 at the critical angle or less (i.e., so that there is noloss due to internal reflection at exit face 55). This is shown in FIG.1A by ray 70 that has angle of incidence 75 relative to sidewall 65 thatis greater than θ_(c) so that ray 70 is reflected to exit face 55 andhas an angle of incidence 80 that is less than or equal to θ_(c). While,in one embodiment, the sidewalls are shaped so that all rays thatencounter the inner surface of the sidewalls experience total internalreflection to exit face 55 and are incident on exit face 55 at thecritical angle or less, other sidewall shapes that allow some loss canbe used.

Turning to FIG. 1B, FIG. 1B is a diagrammatic representation of anotherembodiment of a LED 20. LED 20 comprises a substrate 10 and a quantumwell region 15. Quantum well region 15 includes a light emitting region25, typically a compound semiconductor such as InGaN or AlInGaP orAlGaN. Photons from quantum well region 15 may enter substrate 10through interface 50. In FIG. 1B there may be more losses due to TIR inthe quantum well region because the quantum well region is not shaped toappropriately direct light to interface 50 and/or exit face 55. While inthe embodiments of FIGS. 1A and 1B, some sidewall shapes may not directall the light generated by LED 20 out exit face 55, the portion of lightnot exiting exit face 55 will be emitted from sidewalls 65 and may beemitted near exit face 55, thus allowing for the light generated by LED20 to be captured usefully.

FIG. 4A is a diagrammatic representation of a cross-section of a modelof a LED or a substrate of a LED for determining sidewall shapes.Sidewall shapes can be determined using computer-aided design. A modelof the sidewall can be created in a computer-aided design package andsimulations run to determine an appropriate sidewall shape.

According to one embodiment, each sidewall can be divided into n facetswith each facet being a planar section. For example, sidewall 100 ismade of fifteen planar facets 102 a-102 o rather than a continuouscurve. The variables of each facet can be iteratively adjusted and theresulting distribution profiles analyzed until a satisfactory profile isachieved as described below. While the example of fifteen facets isused, each sidewall can be divided into any number of facets, includingtwenty or more facets.

Each facet can be analyzed with respect to reflecting a certain subsetof rays within a substrate. This area of interest can be defined as an“angular subtense.” The angular subtense for a facet may be defined interms of the angles of rays emanating from a predefined point.Preferably, the point selected is one that will give rays with thehighest angles of incidence on the facet because such rays are the leastlikely to experience TIR at the facet. In a substrate with a squareshaped interface area, for example, this will be a point on the oppositeedge of the interface.

According to one embodiment, for a selected A₁, A₂, and height, themaximum of angle 95 of any ray that will be incident on a given sidewall(e.g., sidewall 100) without being previously reflected by anothersidewall can be determined. In this example, ray 110 emanating frompoint 115 establishes the maximum angle 95 for sidewall 100. If themaximum of angle 95 is 48 degrees and there are 15 facets for sidewall100, each facet (assuming an even distribution of angular subtenses)will correspond to a 3.2 degree band of angle 95 (e.g., a first facetwill be the area on which rays emanating from point 115 with an angle 95of 0-3.2 degrees are incident, the second facet will be the area onwhich rays emanating at point 115 with an angle 95 of 3.2-6.4 degreesare incident, and so on).

For each facet, the exit angle, facet size, tilt angle, or otherparameter of the facet can be set so that all rays incident on the facetexperience TIR and are reflected to exit surface 55 such that they areincident on exit surface 55 with an angle of incidence of less than orequal to the critical angle. Preferably, the sidewalls are also shapedso that a ray viewed in a cross-sectional view only hits a side wallonce. However, there may be additional reflection from a sidewall out ofplane of the section. For a full 3D analysis, a ray that strikes a firstsidewall near a corner, may then bounce over to a second side wall,adjacent to the first, and from there to the exit face. A curve fit orother numerical analysis may be performed to create a curved sidewallshape that best fits the desired facets. In FIG. 4A, for example,sidewall 105 is curved rather than a set of planar facets.

To optimize the variables for each facet, a simulated detector plane 120can be established. Detector plane 120 can include x number of detectorsto independently record incident power. A simulation of light passingthrough the substrate may be performed and the intensity and irradiancedistributions as received by detector plane 120 analyzed. If theintensity and irradiance distributions are not satisfactory for aparticular application, the angles and angular subtenses of the facetscan be adjusted, a new curved surface generated and the simulationre-performed until a satisfactory intensity profile, exitance profile orother light output profile is reached. Additional detector planes can beanalyzed to ensure that both near field and far field patterns aresatisfactory. Alternatively, the simulation(s) can be performed usingthe facets rather than curved surfaces and the surface curves determinedafter a desired light output profile is reached. In yet anotherembodiment, the sidewalls can remain faceted and no curve be generated.

According to another embodiment, the sidewall shape can be selectedbased on multiple parabolas with each planer facet representing a linearapproximation of a portion of a parabola. For example, FIG. 4B is adiagrammatic representation of a portion 400 of a LED. In FIG. 4B, ahypothetical ray 410 is depicted that emanates from the focus 412 of aparabola 415 and intersects sidewall 420 such that it is reflected offsidewall 420 due to TIR and traverses the substrate to intersect exitface 430 at an exit angle 440 that is less than the critical angle andexits the substrate into air or other medium. As can be seen from FIG.4B, at the transition from the substrate to air, ray 410 bends asdescribed by Snell's law. Since the tangent point of the sidewall isdetermined from a parabola and because the ray incident and reflectedoff the sidewall is in the same medium, the ray will be parallel to theoptical axis of the parabola. Thus, light is projected with a half-angle450. Angular subtenses defining the shape of sidewall 420 may beadjusted such that hypothetical ray 410 reflects off sidewall 420 suchthat ray 410 traverses exit face 430 with a desired exit angle 440 orprojects light with a desired half angle 450.

In one embodiment, when fabricating a sidewall or calculating theangular subtense of a sidewall, finer subtenses may be used towards thebase of the sidewall (i.e. nearer the quantum well region) because theeffects of the subtense are greater or more acute upon reflection nearthe base, and thus finer subtenses allow for a sidewall with better TIRproperties, whereas further from the base, where the effects of thesubtenses are less, the subtenses may be coarser. Thus, facets of asidewall may be numerically greater towards the base of a shapedsubstrate LED. In one embodiment, a sidewall may have 20 or more facets,with finer facets at the base of the sidewall, wherein the facetsapproximate one or more subtenses.

A facet can be a linear approximation of a portion 417 of parabola 415.The parameters of parabola 415 can be adjusted until portion 417achieves the desired goal of all rays incident on portion 417 reflectingto exit face 430 such that the rays have an exit angle 440 of less thanthe critical angle. Each facet can be formed from a parabola havingdifferent parameters. Thus, a facet for one angular subtense may bebased on a parabola rather than an adjoining facet. A 20-facet sidewall,for example, may be based on 20 different parabolas.

FIG. 4C is a diagrammatic representation illustrating that the facetsfor a sidewall can be defined using a computer program such as MicrosoftExcel (Microsoft and Excel are trademarks of Redmond, Wash.-basedMicrosoft Corporation). The graphing feature in Microsoft Excel can beused to create a graph, shown at 125, of a sidewall shape. The samegeneral shape can be used for each sidewall or different shapes fordifferent sidewalls. A shaped substrate with the specified sidewallshape (or with a curved sidewall shape based on the specified facets)can be analyzed in, for example, Zemax optical design program (Zemax isa trademark of Zemax Development Corporation of Bellevue, Wash.). Acomputer simulation can be conducted in Zemax to generate a ray traceand an intensity and irradiance distribution profile. If the resultingintensity and irradiance profile has an unsatisfactory distribution orthe transmission efficiency of the shaped substrate is too low, thevariables of the various facets can be adjusted and the simulationsperformed again. This process can be automated through the use of acomputer program to automatically adjust facet variables.

More specifically, FIG. 4C depicts a spreadsheet 500 that can beutilized to design a sidewall shape as shown in graph 510 through thespecification of angular subtenses. Projected half angle column 550contains a plurality of angles that correspond to projected half angle450 of FIG. 4B. Exit angle columns 540 a (in radians) and 540 b (indegrees) contain a plurality of exit angles corresponding to exit angle440 of FIG. 4B. More particularly, all or a subset of the angles incolumn 540 a may be angles that are less than the critical angle suchthat light rays intersecting the exit face at those angles traverse theexit face, exiting the substrate. Columns 540 a and 540 b may beutilized to develop parabola focus column 560, containing a plurality offoci defining different parabolas. Angular subtense column 565 containsa plurality of angles (in radians) that define the limits of an angularsubtense that can be used in conjunction with parabola focus column 560to define the shape of a sidewall such that a ray from the quantum wellregion reflects off the sidewall to exit the exit face at less than thecritical angle. Using the values contained in parabola focus column 560and angular subtense column 565, theta column 570 and radius column 575can be developed wherein corresponding values in columns 570 and 575correspond to points on a desired parabola for the angular subtense. Inturn, theta column 570 and radius column 575 can be utilized to developCartesian coordinates for points on a sidewall (e.g. coordinatetransformation columns 577) that approximate the parabola for theangular subtense.

For example, a user can specify the LED size (i.e., the area of theinterface between the substrate and quantum well region) and thematerial index. Using the example of an LED having a size of 1, and anindex of refraction 1.77, a row in screen 500 can be completed asfollows. The user can specify an exit angle in air (assuming air is themedium in which the LED will operate) in column 550. In the example ofthe first row, the user has selected 55.3792 degrees. The exit angle inthe substrate can be calculated as sin(55.3792/180*π)/1.77 or 0.4649323radians, column 540 a. Column 540 b can be calculated as asin(0.4649323)/π*180=27.2058407. The focus of the parabola can becalculated as 1 (size)/2* (1+cos(π/2−27.2058407/180*π))=0.732466.Angular subtense column 565 can be calculated based on the number in thenext column (representing the relative size of a particular facet) as(90−27.7058047)/20=3.114708. Theta column 570 can calculated using aselected number of facets (in this example 20). For example, in thefirst row theta is calculated as (90−27.7058407)+3.114708*20=124.5883.The radius of the parabola (column 575) for the first facet can becalculated as 2*0.732466/(1+cos(124.5883/180*π)). The contents ofcoordinate transformation columns 577 can be calculated as follows forthe first row: x=−3.3885*cos(124.5883/180*π)=1.923573;y=−3.3885*sin(124.5883/180*π)=2.789594,X=1.923573*cos(27.7058407/180*π)+2.789594*sin(27.7058407/180*π);Y=2.789594*cos(27.7058407/180*π)−1.923573*sin(27.7058407/180*π)−1(size)/2=1.075452and Y′=−Y. The X, Y coordinates can then be used as data point inputsfor a shape fitting chart in Excel. For example graph 510 is based onthe data points in the X and Y columns (with the Y column values used asx-axis coordinates and the X column values used as y-axis coordinates ingraph 510). In addition to the X and Y values a starting value can beset (e.g., 0.5 and 0). The shape from graph 510 can be entered into anoptical design package and simulations run. If a simulation isunsatisfactory, the user can adjust the values in spreadsheet 500 untila satisfactory profile is achieved.

In one embodiment, when a satisfactory light transmission efficiency andirradiance and intensity profiles are achieved, a LED with a substratehaving the specified parameters can be produced. An example of such aLED is shown in FIG. 4D which provides a diagrammatic representation ofone embodiment of a LED having a substrate with sidewalls shaped tocause TIR so that rays are reflected from the sidewalls to the exitsurface. The shape of each sidewall, in this embodiment, is asuperposition of multiple contoured surfaces as defined by the variousfacets. While a curve fit may be performed for ease ofmanufacturability, other embodiments can retain faceted sidewalls. Whilein FIG. 4D, the area of the quantum well region is shown as being squareor rectangular, this is by way of illustration and not limitation. Forexample, the shape of the area of the quantum well region can be any ofa variety of shapes, e.g. circular, rectangular, triangular. Likewise,the shape of the exit face of a LED can be any of a variety of shapes,e.g. circular, rectangular, triangular.

Returning to FIGS. 1A and 1B, as described above with regard to FIGS. 1Aand 1B, various boundary conditions, particularly the area of exit face55 of substrate 10, are determined for substrate 10 so that light isconserved. The minimum area of exit face 55 can be determined from EQN.1 above, which relies on various effective solid angles. Typically, theeffective solid angle of light is determined based on equations derivedfrom idealized sources that radiate as Lambertian emitters, but that aretreated as points because the distances of interest are much greaterthan the size of the source. The observed Radiant Intensity(flux/steradian) of a Lambertian emitter varies with the angle to thenormal of the source by the cosine of that angle. This occurs becausealthough the radiance (flux/steradian/m²) remains the same in alldirections, the effective area of the emitter decreases to zero as theobserved angle increases to 90 degrees from normal. Integration of thiseffect over a full hemisphere results in a projected solid angle valueequal to π steradians.

Turning to FIG. 5, assume a sphere 130 of given radius (R) surroundspoint source 132 (in this example, point source 132 approximates aLambertian source at a significant distance). The projected area of ahemisphere of the sphere is πR² and the projected area of the fullsphere is 2πR². This model can be used to design a LED because aninterface between a quantum well region and a substrate can be modeledas a Lambertian emitter such that from any point on a hypotheticalhemisphere centered over the interface, a given point on the interfacewill have the same radiance. The area A₃ can be calculated as the flat,circular surface (e.g., surface 136) that is subtended by the beam solidangle of interest using a radius of the circle 134 (R_(c)) that is thedistance from the normal ray to the intersection of the sphericalsurface. For a given half angle 137 of θ of the beam, R_(c) is theproduct of R (the radius of the sphere) and the sine of the angle θ,such thatR _(c) =R*Sin(θ)  [EQN. 3]

The area equals:A ₃ =πR _(c) ²=π(R*Sin(θ))²  [EQN. 4A]

The area A₃ is the projected area of the solid angle as it intersectsthe sphere. The area A₃ is divided by the projected area of thehemisphere (A_(h)=πR²) and the quotient is multiplied by the projectedsolid angle of the full hemisphere (equal to π) to obtain the projectedsolid angle Ω, such that:

$\begin{matrix}{\Omega = {\pi*{\begin{Bmatrix}{{projected}\mspace{14mu}{area}\mspace{14mu}{of}} \\{{desired}\mspace{14mu}{solid}\mspace{14mu}{angle}}\end{Bmatrix}/\begin{pmatrix}{{{projected}\mspace{14mu}{area}}\mspace{14mu}} \\{{of}\mspace{14mu}{hemisphere}}\end{pmatrix}}}} & \begin{matrix}\lbrack {{{EQN}.\mspace{14mu} 4}B} \rbrack \\\;\end{matrix} \\\begin{matrix}{\Omega = {(\pi)*\lbrack {\{ {\pi\;( {R*{Sin}\;(\theta)} )^{2}} \}/( {\pi\; R^{2}} )} \rbrack}} \\{= {\pi*{{Sin}^{2}(\theta)}}}\end{matrix} & \begin{matrix}\lbrack {{{EQN}.\mspace{14mu} 4}C} \rbrack \\\lbrack {{EQN}.\mspace{14mu} 5} \rbrack\end{matrix}\end{matrix}$

For interface 50 of FIG. 1, for example, θ is 90 degrees, leading to aprojected solid angle of π*Sin²(90)=π, and for the desired half angle of30 degrees, the projected solid angle is π*Sin²(30)=π/4. Using thesevalues for Ω₁ and Ω₂ for EQN. 1, A₂ can be determined for any halfangle.

In the above example, the solid angle is determined using equationsderived from a Lambertian source modeled as a point source. Theseequations do not consider the fact that light may enter a substrate froma quantum well region through an interface that may be square,rectangular, circular, oval or otherwise shaped. While theabove-described method can give a good estimate of the solid angle,which can be later adjusted if necessary based on empirical or computersimulation testing, other methods of determining the effective solidangle can be used.

FIGS. 6A-6E describe another method for determining the effective solidangle for a substrate of an LED. FIG. 6A is a diagrammaticrepresentation of one embodiment of an interface 150 and an exit face155 of a shaped substrate 160 (shown in FIG. 6B) and a hypotheticaltarget plane 156 onto which light is projected. FIG. 6A illustratesexamples for a position of an effective source origin 152, centralnormal 153 and effective output origin 154. For purposes of furtherdiscussion, it is assumed that the center of interface 150 is at 0,0,0in a Cartesian coordinate system. Target plane 156 represents theparameters of the resulting pattern (e.g., size and half angle used byother optics). According to one embodiment, the half angle at thediagonal (shown as α₁ in FIG. 6B) is the starting point. For example, ifthe desired light at target plane 156 has a maximum half angle of 30degrees, α₁, for a square- or rectangular-faced substrate is 30 degrees.The half-angle within shaped substrate 160 (labeled β₁ and also shown inFIG. 6C) can then be determined according to:n ₂ Sin(α₁)=n ₁ Sin(β₁)  [EQN. 6]

where n₁ is the IOR of shaped substrate 160;

n₂ is the IOR of the material (typically air) into which the light isprojected from shaped substrate 160;

α₁ is the half angle at the exit face in the medium external to thesubstrate (typically air);

β₁ is the desired half angle in the substrate.

For example, if the desired half-angle α₁ is 30 degrees, and a shapedsubstrate having an IOR of 1.77 is projecting into air having an IOR of1, then β₁=16.41 degrees. A similar calculation can be performed for aray projecting from a point on the long and short sides of entrance face150. For example, as shown in FIGS. 6B and 6C, α₂ and β₂ can bedetermined for a ray traveling from the center of one edge on interface150 to the center of the opposite edge of exit face 155. (The criticalangle is the same at 16.41, but β₁ is not the same as β₂. β₂ isdetermined by the geometry of the sides and the height of the shapedsubstrate.)

Using the angles calculated, the location of an effective point sourcecan be determined. For a square interface 150, of length l₁, theeffective point source will be located X=0, Y=0 and

$\begin{matrix}{Z_{eps} = \frac{l_{1}}{\sqrt{2}*\tan\;( \beta_{1} )}} & \lbrack {{EQN}.\mspace{14mu} 7} \rbrack\end{matrix}$

Where Zeps is the distance the effective point source is displaced fromentrance face 150 of shaped substrate 160.

The X, Y and Z distances from the effective point source to points F₁and F₂ can be calculated assuming F₁ intersects a sphere of unity radiusaccording to:X _(F1)=cos(ψ₁)sin(β₁)  [EQN. 8]Y _(F1)=sin(ψ₁)sin(β₁)  [EQN. 9]Z _(F1)=cos(β₁)  [EQN. 10]X_(F2)=0  [EQN. 11]Y _(F2)=cos(ψ₂)*sin(β₁)  [EQN. 12]Z _(F2)=cos(β₁)  [EQN. 13]

where ψ₁ is the angle of the diagonal ray in the X-Y plane (45 degreesfor a square) and where ψ₂=90 degrees for a ray projecting from themiddle of a side parallel to the X axis as shown in FIG. 6C. As shown inFIG. 6A, because 156 intersects the spherical surface at four points andthe magnitude of angle β₂ is less than the magnitude of critical angleβ₁, the values for point F₂ are calculated based on the projection of adiagonal with an angle β₁ onto the plane of the side ray. A similarmethodology based on the geometries previously calculated can be used todetermine other points (e.g., for example, the location of points T₁ andT₂ can be determined based on the location of points F₁ and F₂ and thedesired half angle of light at target plane 156.)

FIG. 6D illustrates the diagonal rays and one ray from the short sideprojected onto a sphere 159 for exit face 155 and sphere 161 for targetplane 156. For exit face 155, the projection of the intersection of theedge rays at the sphere 159 onto the plane of the exit face 155, formselliptical segments. Likewise, the projection of the refracted exit raysat the edge of the target face intersect the sphere 161. FIG. 6E, forexample, points out the circular intersection of the rays lying in theplane formed by the edge 163 of target face 156 intersecting sphere 161(shown at 162), and the projection of that intersection onto the targetplane 156 (shown at 164). By calculating the area of each of theelliptical segments surrounding the square of the target face and addingthat to the area of the target face, we find the total projected area ofthe target face. The effective solid angle can be determined for thetarget plane using EQN. 4B Similarly, by using sphere 159 and theelliptical segments formed thereon by rays, the effective solid anglefor the LED can be determined. For example, the total projected area isdetermined as described above and inserted as “projected area of desiredsolid angle” in EQN. 4B.

As one illustrative example, using the above method to project lightwith a half-angle of 30 degrees using a LED having a substrate with asquare shaped interface and exit face yields an effective solid angle of0.552 steradians to the target in air. By contrast, the use of thetraditional circular projected area with a 30 degree half angleprojection specification would yield an effective solid angle of 0.785steradians. When these values are then used in EQN. 1, for given IORsand flux, the traditional (circular) calculation yields a required exitarea that is undersized by about 30%. If one were to design a systemusing this approach, the applicable physics (i.e. the conservation ofradiance) would reduce the light output by 30% over the optimum design.Conversely, using the corrected effective solid angle described abovecalculates an exit face area that will produce 42% more light outputthan is achievable with the circular calculation.

Although particular methods of determining the effective solid angle fora LED are described above, any method known or developed in the art canbe used. Alternatively, the minimum surface area to conserve light canbe determined empirically. Moreover, while the minimum surface areacalculations above assume light is entering the substrate across theentire surface of the interface between the quantum well region and thesubstrate, in physical devices, light may not enter the substrate in aneven distribution across the entire surface of the interface. Thecalculations of the minimum area of the exit face can be adjusted toaccount for the actual distribution of light traversing the interface,rather than being based entirely on the size of the area of theinterface. In one embodiment, the actual area of the interface throughwhich light enters the substrate can be used as A₁.

Embodiments of LEDs can project light into a desired cone angle of 10-60degrees with a theoretical efficiency of up to 89% (meaning that 89% ofthe light entering the substrate is emitted in the desired half-angleswith 11% fresnel loss) depending on substrate material and Fresnellosses. The efficiency can be 100% without fresnel losses. Even at only70% efficiency, embodiments of LEDs provide greater efficiency thanother LED technologies, while also allowing for uniform or near uniformintensity distributions at both near and far fields.

Fresnel losses at the substrate to air (or other medium) interface canbe overcome by the application of anti-reflective coatings to the exitface of the substrate. Anti-reflective coatings that can be used are anythat would be known to one of ordinary skill in the art and includesingle layer MgO or MgF, multilayer coating or other anti-reflectivecoatings. Through the utilization of anti-reflective coatings, Fresnellosses can be reduced or eliminated, increasing the light outputefficiency of a LED.

An embodiment of a LED may have more than one exit face. For example, ashaped substrate may allow substantially all the light generated by theLED to exit the LED, but through more than a single exit face. FIG. 7 isa diagrammatic representation of an example of a LED 700 with more thanone exit face. In FIG. 7, exit faces 710 a and 710 b of LED 700 areshown. A LED having more than one exit face might emit light into asolid angle greater than a hemisphere. To maximize the light exiting theexit faces, the sidewalls of a substrate with more than a single exitface may have multiple curved or faceted surfaces.

For a LED with two or more exit faces, it is possible for the solidangle of emission of the LED to be greater than a hemisphere (and theprojected solid angle to be greater than pi). An example of this wouldbe if instead of a single planar exit face, the LED had a four sidedpyramidal set of exit faces. If the sidewalls of the substrate of theLED are shaped to direct light entering the substrate through theinterface to one of the four exit faces so as to strike the exit face atan angle not greater than the critical angle, then all the lightentering the substrate may exit the LED through one of the four exitfaces.

Since the faces of the pyramid are not in a plane, but rather are atangles to each other, any ray that strikes an exit face at the criticalangle to that exit face will refract to an exit angle of 90 degrees. Thetotal solid angular space defined this way would then be a function ofthe angular relationship of the four exit faces. To satisfy the etendueequation, the four exit faces in this example would have to have a totalsurface area at least equal to the calculated value using the effectivesolid angle for that construction.

This multi-exit face construction may still be constructed in such a wayas to conserve radiance. That is, by making the total projected exitface area equal to the calculated value, and by designing the sidewallsto provide uniform distribution of the light to each portion of the exitfaces, radiance can be conserved. If the exit faces are made larger thanthe required value, then light entering the substrate may exit throughthe exit faces, with a corresponding reduction in luminous intensity.

A further embodiment of a shaped substrate with multiple exit faces isone in which the sidewalls of the shaped substrate are themselves exitfaces. Depending on a point of entrance of a given light ray, it maystrike a given sidewall at an angle not greater than the critical angle,and pass through that sidewall, or it may strike at an angle greaterthan the critical angle and be internally reflected to another face orsidewall.

If the sidewall exit faces and sidewalls are designed such that any rayentering the substrate from any point on the interface passes through asidewall exit face, then all of the light entering the substrate willexit the substrate.

Shaped substrate LEDs with multiple exit faces may be appropriate foruse in general lighting applications where broad area emission isdesired. Such LEDs may be used in conjunction with additional lens orreflector elements that will direct light produced by the LED into asmaller solid angle.

The potential benefit of a shaped substrate with multiple exit faces orin which sidewalls act as exit faces is that the LED may have a smallervolume or may have a shape that is more readily manufactured—such asplanar faces instead of curved surfaces.

LEDs can be arranged in an array of LEDs. An array of LEDs can be usedto produce a desired amount of light and a desired light pattern. Forexample, LEDs may be arranged in a square or other shape. Using an arrayof LEDs to produce the desired amount of light may be more efficient ormay consume less space than using a single LED. An array of LEDs can beformed during manufacture. For example, an array of LEDs can be formedfrom the same wafer. In FIG. 8A, LED array 800 comprises LEDs 810 a-810c that are formed from the same wafer. Wafer material 820 is removed toform LEDs 810 a-810 c. LED 810 a remains attached to LED 810 b at point830 a. Likewise, LED 810 b remains attached to LED 810 c at point 830 b.Thus, through the selective removal of substrate material, arrays ofLEDs may be formed. FIG. 8 represents one method of forming arrays ofLEDs and is illustrative and not limiting: other methods for formingarrays of LEDs as would be known to one skilled in the art are withinthe scope of the invention.

One advantage of using an array of LEDs is that the shaped substrates ofthe multiple LEDs in the array may be thinner than the shaped substratefor a single LED having the same amount of light output. Additionally,an array of smaller LEDs may be more efficient than a single LED; thatis, an array of smaller LEDs that consume a certain amount of inputpower may produce more light than a single large LED of the same exitface size and input power.

Because some embodiments of LEDs may utilize thicker substrates thantraditional LEDs, a retaining device can be used to secure a LED withinan LED package. A mechanical attachment device (e.g., of molded plastic,metal or other material) can secure an LED or LEDs within an LED packageor other structure and contact an LED to create a normal force to keepthe LED in place. Sideways motion can be prevented by frictional forcebetween the attachment device and the LED. The device may have the sameIOR as the substrate so that rays exiting the substrate are not deviatedas they pass through the attachment device. The attachment device caninclude secondary optics such as a lens, layer of material or other facethrough which light exiting the substrate passes. Consequently, theattachment device can additionally act to shape or further define theoutput beam. FIGS. 9A-9C are diagrammatic representations of variousexamples of retaining devices 900 a-900 c that can be used to secure LED910. Retaining device 900 b of FIG. 9B includes a lens 920 b that canfurther focus light from LED 910. Retaining device 900 c of FIG. 9Cincludes a reflective focusing device 920 c that can further focus lightfrom LED 910. In one embodiment, reflective focusing device 920 c is acompound parabolic concentrator.

One or more methods may be used to shape or form a LED or the substrateof a LED. The methods of shaping a substrate as described below areexemplary and comprise a subset of the numerous methods available. Themethods described below and other methods used in the LED or opticsindustries may be used to produce LEDs. Methods that can be used, aloneor in combination, to shape a LED or a substrate by removing materialinclude etching, laser ablation, water jet cutting, ultrasonic removal,and mechanical removal.

Etching describes a chemical process of removing substrate material in ahighly controlled manner as to yield the appropriate shape. There aretypically two types of etching methods: wet etching and dry etching. Wetetching involves using liquid-phase etchants to remove the substratematerial. In dry etching, plasma etching and reactive ion etching, ionsare created and imparted onto the substrate. There, either based onchemical reaction or particle momentum, material is removed from thesubstrate.

Starting with a wafer of substrate material (that may further includematerial comprising the quantum well region), a particular pattern ofphotoresist can be deposited on a side of the wafer. The wafer is thenetched. Locations on the wafer covered with the photoresist would not beetched, whereas places without the photoresist would have materialremoved. There are many ways to tune the process to achieve the desiredcontour at the edge of the photoresist. For example, thicker layers ofphotoresist can be applied and then sacrificially removed during theetching process, or other sacrificial layers can be used in conjunctionwith the photoresist. These layers are removed over time by the etchantin such a manner as to produce the desired contour of the LED substrate.This can be exploited to accurately etch the wafer so as to produceshaped substrates. Another way is to use multiple resists and multipleetching steps. Each photoresist and etch step can be used to remove asmall layer of material. Multiple small steps can be use get the desired3D shape.

FIG. 10 is a diagrammatic representation of an example of etching. InFIG. 10, wafer 1000 is etched to form shaped substrates 1030 a-1030 c.Photoresist 1010 is applied to a surface of wafer 1000 in a desiredpattern such that portions of the surface of wafer 1000 are covered withphotoresist 1010. Subsequent to the application of photoresist 1010, anetchant is applied to the same surface of wafer 1000 that thephotoresist was applied. The etchant removes substrate material 1020,forming shaped substrates 1030 a-1030 c. Photoresist and etchant can beapplied in successive layers and patterns to achieve a desired sidewallshape.

Etching parameters may be based on the substrate material. The etch ratevaries depending on the etchant and the substrate. For substratematerials used in LED applications such as sapphire and silicon carbide,the etch rates using reactive ion etching can range from 250 nm to 2.5um per min, which may be slow for commercial production purposes.Silicon carbide is on the upper end of the above etch rate whilesapphire is on the lower end.

Laser ablation is the process of using a high power laser to produceLEDs by removing or ejecting quantum well region or substrate material.Each laser pulse will only remove a minute amount of material. The lasercan be translated to remove material with each subsequent pulse. Bytranslating in the X-Y and Z directions, a 3D shape can be removed.Embodiments of laser ablation can be used to shape substrates fasterthan etching. Using known techniques, laser ablation can remove around500 um to 1 mm in thickness per minute in silicon carbide and sapphire.

FIG. 11 is a diagrammatic representation of laser ablation. Laser 1110is applied to wafer 1100 to ablate substrate material 1120, formingshaped substrates 1130 a-1130 b.

A water jet may be used to ablate a wafer to form a substrate of thedesired shape. In one embodiment of water jet ablation, short pulses ofwater can be used to ablate a wafer in stages. The process by whichpulses of water are used to ablate a wafer may be similar to the processdescribed above in regard to laser ablation. In one embodiment of waterjet ablation, the water jet can be used to cut completely through thewafer at a certain angle, then the angle shifted slightly and the waterjet used to cut through the wafer at a slightly higher angle, eventuallyproducing a substrate of the desired shape. In a further embodiment, thewater jet may be charged with abrasive material (e.g. industrial diamondparticles) to increase the rate at which material is ablated.

Another option is to mechanically remove material through grinding,milling, sawing, ultrasonic grinding, polishing, drilling, or othersystems or methods of mechanical removal. There are numerous methods forremoving material to shape one or more LEDs through mechanical removal.For example, a sawing blade (typically, a diamond grinding wheel) can beused to dice the wafer into multiple LEDs or substrates. The saw bladeis prepped to have the inverse shape of one or more sidewalls, takinginto account minor material losses that will occur to the blade duringthe removal process (i.e., the blade may begin slightly oversized). Theblade is then used to saw the wafer. The rotation of the saw blade maypolish the substrate sidewalls as it cuts. Each cut forms the sidewallsof adjacent substrates. According to one embodiment, the saw will firstmake multiple cuts in one-axis and then make cuts orthogonally to thataxis to form the shaped substrates. The mechanical removal of materialmay be done in stages.

FIGS. 12A-12B are diagrammatic representations of forming a LEDutilizing a sawing blade. In FIG. 12A, a sawing blade 1210 having theinverse shape of a desired sidewall of a shaped substrate is applied towafer 1200. FIG. 12B shows sawing blade 1210 when fully impacted intowafer 1200, forming sidewalls 1220 a and 1220 b. FIGS. 13A and 13B arediagrammatic representations of top views of wafer 1200 subsequent tothe application of sawing blade 1210 to wafer 1200. Subsequent to themechanical removal of substrate material, the shaped substrate may bepolished to enhance TIR within the shaped substrate.

While the above methods of ablating a wafer of material to form shapedsubstrates have been described individually, the above methods may becombined. For example, it may be possible to use a combination ofmechanical removal and water jet ablation to ensure an appropriatelycurved sidewall shape. Similarly, various other combinations of methodsand techniques for removing substrate material from a wafer to produceLEDs can be used as appropriate depending on the substrate material. Inaddition, other methods, such as ultrasonic machining can be used toform shaped substrates. Ultrasonic grinding may also be used to shapesubstrates. In embodiments of ultrasonic grinding, a tool with theinverse shape of one or more LEDs is primed with an abrasive and broughtinto contact with the substrate material while the tool isultrasonically vibrated to produce a scrubbing/scuffing action on thesubstrate material such that material is removed and shaped substratesare produced.

While the above embodiments describe forming LEDs from a wafer ofmaterial, shaped substrates utilized to produce LEDs can be formed froma bar of substrate material or may be shaped from substrate materialindividually.

In one embodiment of a LED, LEDs may be individually produced. Forexample, an individual shaped substrate may be mounted in a receivingtool such that it is accurately located. The sidewalls may be protectedby protectors such as resist materials, shielding structures in thereceiving tool or other protectors. The desired epitaxial layers may bedeposited on the base of the shaped substrate, thus producing a LED. Byway of further example, the individual shaped substrate may be made of amoldable material such as high temperature glass. The glass shapedsubstrate may then be developed into a LED by depositing the desiredepitaxial layers on the base using low temperature epitaxial growthmethods.

In some cases, it may be desired to generate white light using a LED.This can be accomplished by impinging light from a single-color (e.g.blue), short wavelength LED onto phosphors or other particles thatabsorb the light and re-emit light in a wavelength that the human eyeperceives as white light. Phosphors or other particles can be used withembodiments of LEDs to produce white light. FIG. 14 shows one embodimentof LED 20. Phosphors or other particles can be placed at interface 50between quantum well region 15 and substrate 10. In such a case, thelight entering substrate 10 would be white light as seen by the humaneye. Phosphors can also be placed subsequent to exit face 55 ofsubstrate 10. According to one embodiment, a layer of particles can coatexit face 55. According to other embodiments, particles can be onanother piece of material that contacts the exit face or that is offsetfrom the exit face. For example, phosphors can be on an interior face ofa lens that encapsulates, but does not contact, exit face 55 of LED 20.

Coating the exit face or faces of a LED may have fabrication advantagesthat may allow for the simplification of white light LED fabrication,which may in turn reduce the cost of white light LED fabrication. Forexample, a side of a wafer out of which shaped substrate LEDs will beformed may be coated with a layer containing phosphors or otherparticles (i.e. a particle coating) that can be excited to emit whitelight. The side of the wafer that has not been coated with the particlecoating can be ablated. When the wafer has been ablated to producemultiple LEDs, the LEDs will have an exit face having the particlecoating necessary to produce white light. Furthermore, because a shapedsubstrate directs a supermajority of light entering the substrate to aknown exit face or faces, coating a particular exit face or faces may behighly effective in the generation of white light. Accordingly, the useof a shaped substrate may eliminate the need to coat the sidewalls or aportion of the sidewalls of an LED with a particle coating. Thus, therewill be no need to individually apply a particle coating to each LED.Applying a particle coating to a side of a wafer may be cheaper thanapplying a particle coating to individual LEDs. The sidewalls of thesubstrate can be designed so that light scattered back into thesubstrate by interactions with the particle coating may be partially orfully recycled. Utilizing nano-particles to generate white light inconjunction with a LED allows for minimum deflection of light, thusminimizing backscattered light and maximizing the light emitted from theexit face.

Heat generated in the quantum well region of LEDs causes the degradationof phosphor particles or nano-particles. In current LEDs, phosphorsconformally coat the LED chip. The thermal density is highest at thechip, and therefore phosphors are subject to tremendous heat. Inembodiments of an LED with a shaped substrate having a phosphor coatingon the exit face, because the exit face is removed from the heatgenerating quantum well region by the height of the substrate, thedegradation of the phosphors is reduced. Thus, an LED with a thicksubstrate and consequently an exit face removed from the quantum wellregion may generate white light of a desired quality longer thanexisting designs.

Potential applications for embodiments of LEDs include cell phonedisplay lighting. Present systems typically use three side-emitting blueLEDs with phosphor-filled encapsulant material to generate white light.The sides of the LED are typically opaque and a large percentage of thelight generated is absorbed by the sidewalls. This results in over 50%of the light being lost to absorption. In addition, the index change atthe interface of the encapsulant to air creates a TIR condition for exitrays striking the interface at greater than the critical angle. Thisresults in approximately 44% loss at the interface. Embodiments ofshaped substrate LEDs, can deliver 80% of the generated light to thelight guide, resulting in very large system brightness improvements.

Another potential application for embodiments of LEDs is use as a cellphone camera flash. Present systems typically use LEDs with Gaussianenergy distributions that produce a very bright area in the center ofthe image and dark areas at the edges, causing uneven lighting of thesubject matter. Moreover, the beam shape of present flash units iscircular, while the image captured by the CCD camera is rectangular.Additionally, the index of refraction change at the interface of theencapsulant to air creates a TIR condition for exit rays striking theinterface at greater than the critical angle. This results in losses atthe interface that are a function of the exit solid angle. Embodimentsof LEDs, on the other hand, can deliver a rectangular or square flash,with 80% of the light entering the substrate of the LED being providedto the image area in a uniform distribution. This results in moreuniform scene illumination and higher levels of illumination as opposedto prior art LED flash systems.

Another potential application for embodiments of LEDs is for liquidcrystal display (“LCD”) backlighting. Traditional LCD systems use alinear array of red, green and blue LEDs. The light from the LEDs isdirected into a mixing light guide to provide uniformity of color andintensity. Typically, the LEDs have a dome placed over the LED and lightis captured by elliptical reflectors to direct the light to the lightguide. While elliptical reflectors work well for point sources, LEDs arenot point sources and some of the rays will not get to the focii insidethe light guide. Moreover, since some light from a dome encapsulant isemitted at greater than 180 degrees, some of the light is absorbed bythe substrate, PCB board and other components. Furthermore, because thedome is large with respect to the size of the cavity in the dome, acertain percentage of light typically gets refracted. Because theselosses are multiplicative, only a percentage of the light originallyemitted from the LED actually gets to the light guide.

Embodiments of LEDs, on the other hand, can provide up to 80% of thelight entering the substrate of the LED to the light guide (assumingFresnel losses) in the desired cone angle. Consequently, lower powerLEDs can be used to achieve the same results as are possible in currentsystems or more light can be delivered at the same power consumptionlevel. Indeed, in some embodiments, the light guide may not be requiredand arrays of LEDs may be used to directly backlight LCDs.

Another potential use for embodiments of LEDs is in car headlights,flashlights, digital light processing (“DLP”) systems and other devices.The shape of the LED can be selected so as to provide the desiredprojection cone and beam profile. Furthermore, the combination of a LEDand a condenser lens or other optical device, such as the Primary OpticDevice (“POD”) described in U.S. patent application Ser. No. 11/649,018,entitled “SEPARATE OPTICAL DEVICE FOR DIRECTING LIGHT FROM AN LED”,allows for the emission of a narrow solid angle (on the order of 0.1steradians or less) while conserving radiance and doing so in a verysmall volume. Such a combination is applicable for flashlights, spotlights or any other narrow beam application.

In U.S. patent application Ser. No. 11/649,018, entitled “SEPARATEOPTICAL DEVICE FOR DIRECTING LIGHT FROM AN LED”, a Primary Optic Device(“POD”) is described. Embodiments of systems and methods describedherein differ from and provide significant advantages over the PODdevice. The POD device is a passive optic element used in conjunctionwith LEDs to focus light emitted from the LED. The POD device itself isunable to generate light and directs light generated by other sources.The POD is typically made of materials having an IOR of approximately1.5. Thus, the amount of light that can enter the POD device from an LEDis limited by the change in IOR from the LED material to the POD devicematerial. By contrast, this disclosure regards a LED that itselfcollects and directs the light generated in its own quantum wells. Allof the light in the substrate of the LED can theoretically be capturedand directed. If the substrate material has a higher IOR than or equalIOR to the IOR of the quantum well region material, then all of thelight generated by the quantum wells of the LED may be captured anddirected. With the POD device, this may not be possible. Shaping an LEDto capture and direct the light generated by the quantum wells of theLED itself results in a single LED that may be used in many applicationswithout the need for additional optic components.

FIGS. 15A and 15B are a diagrammatic representations of anotherembodiment of a layout of multiple die being made in a single wafer1500. In this case, the die are packed more closely together and thesidewall shape is formed by any of the methods already described, exceptthe depth of cut of the sidewall is greatly reduced. For example for a 3mm thick wafer in the previous embodiment, the sidewall shape would becut 2.75 mm deep with 0.25 mm remaining to hold all the die together. Inthe example of FIG. 15, the depth of cut is only about 1 mm, leavingabout 2 mm to hold the die together. This creates a much stronger waferfor handling in manufacturing, and allows the die to packed more closelytogether. This results in more die per wafer on the order of 1.5 to 2.4times as many die per wafer. After all the operations are completed onthe wafer, the die are separated for example by diamond sawing them witha thin sawblade (on the order of 0.1 mm wide. The surface produced bythe sawblade may closely approximate the intended sidewall shape in thatregion, and may provide an adequately polished surface, such that nofurther operations are needed. Alternatively, subsequent operations maybe performed to finish shaping and polishing that portion of thesidewalls, on the individual die.

While this disclosure describes particular embodiments, it should beunderstood that the embodiments are illustrative and that the scope ofthe invention is not limited to these embodiments. Many variations,modifications, additions and improvements to the embodiments describedabove are possible. For example, the various ranges and dimensionsprovided are provided by way of example and LEDs may be operable withinother ranges using other dimensions. By way of example, while shapedsubstrates have been described in regard to sapphire and siliconcarbide, other substrates that allow the passage of light may be used.For example, substrates may be made of glass or diamond. In oneembodiment, substrates may be molded from moldable glass, providing acost effective and easily shaped substrate. It is contemplated thatthese variations, modifications, additions and improvements fall withinthe scope of the invention as detailed in the following claims.

1. A method of manufacturing an LED comprising: determining a size of anexit face of a shaped substrate portion of the LED so that the exit facehas at least 70% of a minimum area necessary to conserve radiance for adesired half-angle of light projected from the LED; determining adistance between the exit face and an interface between the shapedsubstrate portion and a quantum well region of the LED; determiningshapes and positions of a set of sidewalls of the shaped substrateportion of the LED so that each sidewall is positioned and shaped tocause at least a majority of rays having a straight transmission pathfrom the interface to that sidewall to reflect through total internalreflection to the exit face with an angle of incidence at the exit faceat less than or equal to a critical angle at the exit face; and formingthe shaped substrate portion of the LED in accordance with thedetermined size of the exit face, shapes and positions of the set ofsidewalls and distance between the exit face and the interface; whereinthe method is performed by performing steps in the order of: (a)determining boundary conditions for the shaped substrate portion of theLED, wherein the boundary conditions comprise the size of the exit faceof the shaped substrate portion of the LED and the distance between theexit face and the interface between the shaped substrate portion and thequantum well region of the LED; (b) the determining the shapes andpositions of the set of sidewalls of the shaped substrate portion of theLED; and (c) the forming the shaped substrate portion of the LED.
 2. Themethod of claim 1, depositing one or more layers on the shaped substrateportion to form the quantum well region of the LED after the shapedsubstrate portion has been formed.
 3. The method of claim 1, furthercomprising: providing a substrate and one or more layers for a quantumwell region of the LED; removing material from the substrate to form theshaped substrate portion of the LED.
 4. The method of claim 3, whereinremoving material from the substrate further comprises removing materialusing one of an ultrasonic removal process; laser ablation or water jetcutting.
 5. The method of claim 3, wherein removing material from thesubstrate further comprises cutting or grinding the substrate with ablade having an inverse shape to a desired shape of the shaped substrateportion of the LED.
 6. The method of claim 3, wherein removing materialfrom the substrate further comprises etching the substrate.
 7. Themethod of claim 3, further comprising coating the substrate with aphoto-luminescent layer prior to removing material from the substrate.8. The method of claim 1, further comprising shaping the quantum wellregion of the LED in conjunction with shaping the substrate.
 9. Themethod of claim 1, wherein the LED is shaped to achieve a desired lightoutput profile.
 10. The method of claim 1, wherein the size of the exitface is selected to have at least the minimum area necessary to conserveradiance.
 11. A method of shaping an LED comprising: providing a wafercomprising a substrate and one or more layers for a quantum well regionof the LED; grinding the substrate to form a shaped substrate portion ofthe LED; wherein the shaped substrate portion is shaped to comprise: anexit face opposite from and a distance from an interface with the toreceive light generated by a quantum well region of the LED, the exitface having a size being at least 70% of a minimum area necessary toconserve radiance for a desired half-angle of light projected from theshaped substrate; and a set of sidewalls, wherein each sidewall ispositioned and shaped so that at least a majority of rays having astraight transmission path from the interface to that sidewall reflectthrough total internal reflection to the exit face with an angle ofincidence at the exit face of less than or equal to a critical angle atthe exit face; wherein the method is performed by performing steps inthe order of: (a) determining boundary conditions for the shapedsubstrate portion of the LED, wherein the boundary conditions comprisethe size of the exit face of the shaped substrate portion of the LED andthe distance between the exit face and the interface between the shapedsubstrate portion and the quantum well region of the LED; (b)determining the shapes and positions of the set of sidewalls of theshaped substrate portion of the LED; and (c) shaping the shapedsubstrate portion of the LED.
 12. The method of claim 11, whereingrinding the substrate comprises grinding the substrate with a shapeddiamond grinding wheel.
 13. The method of claim 11, wherein grinding thesubstrate comprises: making multiple cuts in the substrate along a firstaxis at least part way through the wafer; and making multiple cuts inthe substrate along a second axis at least part way through the wafer atan angle to the first axis to create shaped substrate portions formultiple LEDs.
 14. The method of claim 11, further comprising shapingthe quantum well region of the LED in conjunction with shaping thesubstrate.
 15. The method of claim 11, wherein the LED is shaped toachieve a desired light output profile.
 16. The method of claim 11,wherein the exit face has the minimum area necessary to conserveradiance.
 17. A method of shaping an LED comprising: providing a wafercomprising a substrate and one or more layers for a quantum well regionof the LED; etching the substrate to form a shaped substrate portion ofthe LED; wherein the shaped substrate portion of the LED is shaped tocomprise: an exit face opposite and at a distance from an interface toreceive light generated by a quantum well region of the LED, the exitface having at least 70% of a minimum area necessary to conserveradiance for a desired half-angle of light projected from the shapedsubstrate portion of the LED; and a set of sidewalls, wherein eachsidewall is positioned and shaped so that at least a majority of rayshaving a straight transmission path from the interface to that sidewallreflect through total internal reflection to the exit face with an angleof incidence at the exit face of less than or equal to a critical angleat the exit face; wherein the method is performed by performing steps inthe order of: (a) determining boundary conditions for the shapedsubstrate portion of the LED, wherein the boundary conditions comprisethe size of the exit face of the shaped substrate portion of the LED andthe distance between the exit face and the interface between the shapedsubstrate portion and the quantum well region of the LED; (b)determining the shapes and positions of the set of sidewalls of theshaped substrate portion of the LED; and (c) shaping the shapedsubstrate portion of the LED.
 18. The method of claim 17, whereinetching the substrate further comprises dry etching the substrate. 19.The method of claim 17, wherein etching the substrate further compriseswet etching the substrate.
 20. The method of claim 17, wherein etchingthe substrate further comprises etching the substrate using a multipleetch resist etching process.
 21. The method of claim 17, furthercomprising shaping the quantum well region of the LED in conjunctionwith shaping the substrate.
 22. The method of claim 17, wherein the LEDis shaped to achieve a desired light output profile.
 23. The method ofclaim 17, wherein the exit face is shaped to have at least the minimumarea necessary to conserve radiance.
 24. A method of manufacturing anLED comprising: providing a substrate and one or more layers for aquantum well region of the LED; removing material from the substrate toform a shaped substrate portion of the LED, the shaped substrate portioncomprising: two or more exit faces having a size such that a combinedarea of the two or more exit faces being at least 70% of a minimum areanecessary to conserve radiance for a desired half-angle of lightprojected from the LED; and a set of sidewalls, wherein each sidewall ispositioned and shaped so that at least a majority of rays having astraight transmission path from an interface to that sidewall reflectthrough total internal reflection to an exit face of the two or moreexit faces with an angle of incidence at that exit face of less than orequal to a critical angle at that exit face; wherein the method isperformed by performing steps in the order of: (a) determining boundaryconditions for the shaped substrate portion of the LED, wherein theboundary conditions comprise the size of the two or more exit faces ofthe shaped substrate portion of the LED and the distance between the twoor more exit faces and the interface between the shaped substrateportion and the quantum well region of the LED; (b) determining theshapes and positions of the set of sidewalls of the shaped substrateportion of the LED; and (c) shaping the substrate portion of the LED.25. The method of claim 24, wherein the two or more exit faces have anarea that is at least the minimum area necessary to conserve radiance.